One of the trends of development of the internal combustion engine generally has been to improve the efficiency thereof in such a way as to afford either improved fuel consumption or improved power output. Along those lines, one form of internal combustion piston engine, which can also be referred to as a reciprocating engine, for operation with gaseous and/or liquid fuel, which can be referred to generally for the sake of simplicity as a fluid fuel, comprises a fuel supply system which for compressing the fuel for each working cylinder of the engine has a piston-type compressor associated with the working cylinder at the cylinder head end thereof, the piston compressor comprising a compressor cylinder and a stepped or differential piston which is axially movably accommodated in the compressor cylinder and the larger area of which is subjected to the pressure of the combustion chamber of the associated working cylinder. The smaller area or surface of the stepped or differential piston of the respective piston compressor compresses the fuel when the pressure rises in the combustion chamber of the associated working cylinder. That arrangement comprises at least one flow transfer path which extends between a compression chamber of the piston compressor and the combustion chamber of the associated working cylinder and which has at least one opening or port into the combustion chamber. The port is disposed in the path of movement of the stepped or differential piston of the piston compressor and can be opened and closed by a control edge of that piston. An engine design configuration of that kind is to be found in German patent specification No. 2 826 807. In operation of that engine, in successive working cycles of the engine fuel in gaseous form is compressed by means of the respective piston compressor arranged in the cylinder head of a working cylinder, more specifically with its differential piston which can be subjected to the pressure in the combustion chamber at the larger area of the differential piston, with the fuel being injected, in accordance with a law which is not of specific interest in the present context, in a compressed and accordingly heated condition, into combustion air which is compressed in the combustion chamber of the associated working cylinder itself. The return movement of the compressor piston for a fresh working cycle thereof, and thus the intake of fuel into the compression chamber of the compressor, by a suction effect, are produced by means of a spring arrangement supporting the piston at the rear thereof, or by some other form of actuation thereof, providing for displacement thereof in the opposite direction to the compression stroke movement, when a low pressure obtains in the combustion chamber of the working cylinder of the engine.